There is a Yahoo Group for Mental Health Billing (PM me if you can't find a like through Dr. Google), and there have been quite a few discussions about billing/scheduling software options out there.
Electronic Medical Record software.....There are *huge* differences in cost & functionality...so shop wisely. I have used 2 versions of EPIC at my last two Uni hospitals, and I have mixed reviews. Cost-wise I don't think they are worth it, as they are stupid expensive and require updates, but for the scale of the hospital systems it was basically required. Ironically, CPRS (VA system) was a frankenstein program (all patched together and ugly), but it worked pretty well. Billing was integrated into the EMR and scheduling somehow integrated too (but I think there was a lot more support staff to make that portion work). The above are true electronic medical record systems that integrate all sorts of bells and whistles.
There are smaller/cheaper/free software options that can address individual needs like billing, scheduling, etc....but an "All-in-one" solution will be pricey and usually a compromise in one or more areas.
Billing....Office Ally, which can be free to the user to submit billing for insurance (there is a cap on the # of Medicare pts per month before it costs a charge), but they are very well regarded in the PP sector for psych. Many places offer trials, but for larger systems (more than a 5-10 clinician group practice) it isn't really feasible. In my former life we built a few difference systems for boutique places, but that option is very niche....since off the shelf is cheaper and enterprise systems are more robust but MUCH more costly.
Scheduling....not sure. I use EPIC (out-pt...still being implemented) and Google Calendar (w. FT admin staff, also for out-pt), but no identifiable information can be posted, which can be tricky and a hassle.
I'm not sure there are perfect solutions for either, but if you can figure out "good enough" for your budget, that is probably the best you can hope for with this stuff. Scalability is really going to be the primary factor limiting your choices. If you are looking for a <$1k solution v. $5k v. $100k v. $1m+. Yes...they get 7 figure. Nuts.
*edited to clarify a couple of things*